11X1 T17 01 area under curve

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<ul><li> 1. Integration Area Under Curve </li></ul> <p> 2. Integration Area Under Curve 3. Integration Area Under Curve 4. Integration Area Under CurveArea 11 12 33 5. Integration Area Under CurveArea 11 12 33Area 9 6. Integration Area Under CurveArea 11 12 33Area 9 7. Integration Area Under Curve10 11 Area 11 12 3333 Area 9 8. Integration Area Under Curve10 11 Area 11 12 3333 1 Area 9 9. Integration Area Under Curve10 11 Area 11 12 3333 1 Area 9Estimate Area 5 unit 2 10. Integration Area Under Curve10 11 Area 11 12 3333 1 Area 9Estimate Area 5 unit 2Exact Area 4 unit 2 11. Area 0.40.43 0.83 1.23 1.63 23 12. Area 0.40.43 0.83 1.23 1.63 23 Area 5.76 13. Area 0.40.43 0.83 1.23 1.63 23 Area 5.76 14. 0.403 0.43 0.83 1.23 1.63 Area 0.40.43 0.83 1.23 1.63 23 Area 5.76 15. 0.403 0.43 0.83 1.23 1.63 Area 0.40.43 0.83 1.23 1.63 23 2.56 Area 5.76 16. 0.403 0.43 0.83 1.23 1.63 Area 0.40.43 0.83 1.23 1.63 23 2.56 Area 5.76Estimate Area 4.16 unit 2 17. Area 0.20.23 0.43 0.63 0.83 13 1.23 1.43 1.63 1.83 23 18. Area 0.20.23 0.43 0.63 0.83 13 1.23 1.43 1.63 1.83 23 Area 4.84 19. Area 0.20.23 0.43 0.63 0.83 13 1.23 1.43 1.63 1.83 23 Area 4.84 20. 0.203 0.23 0.43 0.63 0.83 13 1.23 1.43 1.63 1.83 Area 0.20.23 0.43 0.63 0.83 13 1.23 1.43 1.63 1.83 23 Area 4.84 21. 0.203 0.23 0.43 0.63 0.83 13 1.23 1.43 1.63 1.83 Area 0.20.23 0.43 0.63 0.83 13 1.23 1.43 1.63 1.83 23 3.24 Area 4.84 22. 0.203 0.23 0.43 0.63 0.83 13 1.23 1.43 1.63 1.83 Area 0.20.23 0.43 0.63 0.83 13 1.23 1.43 1.63 1.83 23 3.24 Area 4.84 Estimate Area 4.04 unit 2 23. As the widths decrease, the estimate becomes more accurate, lets investigate one of these rectangles. y y = f(x) x 24. As the widths decrease, the estimate becomes more accurate, lets investigate one of these rectangles. y y = f(x) x 25. As the widths decrease, the estimate becomes more accurate, lets investigate one of these rectangles. y y = f(x) c x A(c) is the area from 0 to c 26. As the widths decrease, the estimate becomes more accurate, lets investigate one of these rectangles. y y = f(x) cxx A(c) is the area from 0 to cA(x) is the area from 0 to x 27. A(x) A(c) denotes the area from c to x, and can be estimated by the rectangle; 28. A(x) A(c) denotes the area from c to x, and can be estimated bythe rectangle;f(x)x-c 29. A(x) A(c) denotes the area from c to x, and can be estimated bythe rectangle;f(x) x-c A x Ac x c f x 30. A(x) A(c) denotes the area from c to x, and can be estimated bythe rectangle;f(x) x-c A x Ac x c f x A x Ac f x xc 31. A(x) A(c) denotes the area from c to x, and can be estimated bythe rectangle;f(x) x-c A x Ac x c f x A x Ac f x xcAc h Ac h = width of rectangleh 32. A(x) A(c) denotes the area from c to x, and can be estimated bythe rectangle;f(x) x-c A x Ac x c f x A x Ac f x xcAc h Ac h = width of rectangleh As the width of the rectangle decreases, the estimate becomes more accurate. 33. i.e. as h 0, the Area becomes exact 34. i.e. as h 0, the Area becomes exactAc h Ac f x lim h 0h 35. i.e. as h 0, the Area becomes exact Ac h Ac f x limh 0 h A x h A x lim h 0 as h 0, c x h 36. i.e. as h 0, the Area becomes exact Ac h Ac f x limh 0 h A x h A x lim h 0 as h 0, c x h A x 37. i.e. as h 0, the Area becomes exact Ac h Ac f x limh 0 h A x h A x lim h 0 as h 0, c x h A x the equation of the curve is the derivative of the Area function. 38. i.e. as h 0, the Area becomes exact Ac h Ac f x limh 0 h A x h A x lim h 0 as h 0, c x h A x the equation of the curve is the derivative of the Area function.The area under the curve y f x between x a and x b is; 39. i.e. as h 0, the Area becomes exact Ac h Ac f x limh 0 h A x h A x lim h 0 as h 0, c x h A x the equation of the curve is the derivative of the Area function.The area under the curve y f x between x a and x b is; bA f x dx a 40. i.e. as h 0, the Area becomes exact Ac h Ac f x limh 0 h A x h A x lim h 0 as h 0, c x h A x the equation of the curve is the derivative of the Area function.The area under the curve y f x between x a and x b is; bA f x dx a F b F a 41. i.e. as h 0, the Area becomes exact Ac h Ac f x limh 0 h A x h A x lim h 0 as h 0, c x h A x the equation of the curve is the derivative of the Area function.The area under the curve y f x between x a and x b is; bA f x dx a F b F a where F x is the primitive function of f x 42. e.g. (i) Find the area under the curve y x 3 , between x = 0 andx= 2 43. e.g. (i) Find the area under the curve y x 3 , between x = 0 and2x= 2A x 3 dx 0 44. e.g. (i) Find the area under the curve y x 3 , between x = 0 and2x= 2A x 3 dx 02 x4 1 4 0 45. e.g. (i) Find the area under the curve y x 3 , between x = 0 and2x= 2A x 3 dx 0 2 x4 1 4 0 2 04 1 4 4 46. e.g. (i) Find the area under the curve y x 3 , between x = 0 and2x= 2A x 3 dx 0 2 x4 1 4 0 2 04 1 4 4 4 units 2 47. e.g. (i) Find the area under the curve y x 3 , between x = 0 and2x= 2A x 3 dx 0 2 x4 1 4 0 2 04 1 4 4 4 units 2 3 ii x 2 1dx 2 48. e.g. (i) Find the area under the curve y x 3 , between x = 0 and2x= 2A x 3 dx02 x4 14 0 2 04 1 44 4 units 2 3 3ii x 1dx 2 1 x 3 x 2 2 3 49. e.g. (i) Find the area under the curve y x 3 , between x = 0 and2x= 2A x 3 dx 0 2 x4 1 4 0 2 04 1 4 4 4 units 2 33ii x 1dx 2 1 x 3 x 2 2 3 1 33 3 1 2 3 2 3 3 50. e.g. (i) Find the area under the curve y x 3 , between x = 0 and2x= 2A x 3 dx 0 2 x4 1 4 0 2 04 1 4 4 4 units 2 33ii x 1dx 2 1 x 3 x 2 2 3 1 33 3 1 2 3 2 3 3 22 3 51. 5 iii x 3dx4 52. 55 1 2 iii x dx x 3 4 2 4 53. 55 1 2 iii x dx x 3 4 2 4 11 1 2 2 2 5 4 9800 54. 55 1 2 iii x dx x 3 4 2 4 2 2 1 1 1 2 5 4 9800Exercise 11A; 1Exercise 11B; 1 aefhi, 2ab (i,ii), 3ace, 4b, 5a, 7* </p>